Sunrise & Sunset Calculator

Calculate Sunrise & Sunset Times

Enter your location’s coordinates and the date to find out when the sun will rise and set. This tool demonstrates how to calculate sunrise and sunset using latitude longitude for any location on Earth.

Example Sunrise & Sunset Times Around the World

City	Latitude	Longitude	Approx. Sunrise (Local Time)	Approx. Sunset (Local Time)
Tokyo, Japan	35.6895	139.6917	–:–	–:–
Sydney, Australia	-33.8688	151.2093	–:–	–:–
Cairo, Egypt	30.0444	31.2357	–:–	–:–
London, UK	51.5074	-0.1278	–:–	–:–
Rio de Janeiro, Brazil	-22.9068	-43.1729	–:–	–:–

The table above shows estimated sunrise and sunset times for major international cities on the selected date, demonstrating the impact of geographic location.

Understanding the celestial mechanics behind the rising and setting of the sun is not just for astronomers. For photographers, travelers, and the curious-minded, knowing how to calculate sunrise and sunset using latitude longitude is a powerful skill. This article demystifies the entire process, from the core formulas to practical application.

What is the Sunrise and Sunset Calculation?

The method to how to calculate sunrise and sunset using latitude longitude is a series of mathematical steps that model the Earth’s rotation relative to the sun. It determines the precise moments the upper limb of the Sun appears on the horizon (sunrise) and disappears below it (sunset). This calculation is essential for navigation, astronomy, and daily planning. Anyone from a farmer planning their day to a filmmaker chasing the golden hour can benefit from this knowledge. A common misconception is that the sun rises exactly in the east and sets exactly in the west every day; in reality, this only happens on the equinoxes.

The Formula and Mathematical Explanation for How to Calculate Sunrise and Sunset Using Latitude Longitude

The core of the calculation lies in the “Sunrise Equation.” It may look intimidating, but it’s a logical progression. Here’s a step-by-step breakdown of how to calculate sunrise and sunset using latitude longitude.

1. Calculate Day of the Year (N): Convert the date into a number from 1 (Jan 1) to 365/366.
2. Approximate Time of Transit: Calculate an approximation of the sun’s transit (solar noon) based on the longitude.
3. Calculate Sun’s Mean Anomaly (M): This is the position of Earth in its orbit around the Sun, assuming a perfectly circular orbit.
4. Calculate Sun’s True Longitude (L): Adjust the mean anomaly to account for Earth’s elliptical orbit.
5. Calculate Sun’s Right Ascension (RA): Project the sun’s position onto the celestial equator.
6. Calculate Sun’s Declination (δ): This is the sun’s angle above or below the celestial equator, which changes with the seasons due to Earth’s axial tilt.
7. Calculate Hour Angle (H): This is the key. The hour angle is the angular distance between the sun’s current position and its position at solar noon. The sunrise equation, cos(H) = [-sin(0.833°) – sin(φ) * sin(δ)] / [cos(φ) * cos(δ)], is used here, where φ is latitude. The -0.833° accounts for atmospheric refraction and the sun’s radius.
8. Calculate Sunrise and Sunset in UTC: Use the hour angle to determine the time from solar noon to sunrise and sunset, then convert to UTC.
9. Convert to Local Time: Adjust the UTC time based on the local time zone offset.

This process provides a robust method for how to calculate sunrise and sunset using latitude longitude with high accuracy.

Variable Explanations

Variable	Meaning	Unit	Typical Range
φ (phi)	Observer’s Latitude	Degrees	-90° to +90°
λ (lambda)	Observer’s Longitude	Degrees	-180° to +180°
N	Day of the Year	Integer	1 to 366
δ (delta)	Solar Declination	Degrees	-23.44° to +23.44°
H	Hour Angle	Degrees	-180° to +180°

Practical Examples (Real-World Use Cases)

Example 1: Summer Solstice in Paris

An outdoor event planner in Paris wants to know the exact sunset time on June 21st to schedule a fireworks display. They need to know how to calculate sunrise and sunset using latitude longitude for their planning.

• Inputs: Latitude: 48.8566° N, Longitude: 2.3522° E, Date: June 21
• Calculation: The calculator finds the day of the year, high positive solar declination (approx. +23.44°), and computes the hour angle.
• Outputs: Sunrise is very early (e.g., ~5:47 AM), and sunset is very late (e.g., ~9:58 PM), resulting in a long daylight duration. This allows the planner to schedule the fireworks for well after 10:00 PM to ensure complete darkness.

Example 2: Winter in Ushuaia

A tourist visiting Ushuaia, Argentina, the “End of the World,” in July wants to plan their sightseeing. Knowing how to calculate sunrise and sunset using latitude longitude is crucial for making the most of the limited daylight.

• Inputs: Latitude: -54.8019° S, Longitude: -68.3030° W, Date: July 15
• Calculation: With a high southern latitude in winter, the solar declination is highly negative from Ushuaia’s perspective.
• Outputs: The calculator shows a very late sunrise (e.g., ~9:55 AM) and a very early sunset (e.g., ~5:20 PM). The daylight duration is extremely short, so the tourist must plan activities within this tight window. This demonstrates the dramatic effect of latitude when you calculate sunrise and sunset using latitude longitude.

How to Use This Sunrise and Sunset Calculator

Our calculator makes it easy to apply the principles of how to calculate sunrise and sunset using latitude longitude.

1. Enter Latitude: Input the latitude of your location. North is positive, South is negative.
2. Enter Longitude: Input the longitude. East is positive, West is negative.
3. Select Date: Choose the desired date from the calendar.
4. Read the Results: The calculator instantly displays the local sunrise and sunset times. The intermediate results like Day of the Year and Solar Declination provide insight into the calculation.
5. Analyze the Chart: The daylight chart shows the trend, helping you understand if days are getting longer or shorter. Using this tool is the simplest way to see the results of the complex process behind how to calculate sunrise and sunset using latitude longitude.

Key Factors That Affect Sunrise and Sunset Results

• Latitude: The most critical factor. The further from the equator, the greater the variation in day length throughout the year.
• Longitude: This determines the timing within a time zone. Locations on the eastern edge of a time zone see sunrise earlier than those on the western edge.
• Day of the Year (Season): This determines the sun’s declination. The Earth’s 23.5° axial tilt is the reason for the seasons and the changing sunrise/sunset times. Understanding this is key to how to calculate sunrise and sunset using latitude longitude.
• Time Zone: The final calculated UTC time must be converted to the correct local time zone. Daylight Saving Time further complicates this.
• Altitude/Elevation: Higher elevations experience sunrise slightly earlier and sunset slightly later because the horizon is lower. Our calculator uses a sea-level horizon.
• Atmospheric Refraction: The Earth’s atmosphere bends light, making the sun appear on the horizon when it is geometrically still below it. This effect is accounted for in accurate calculations.

Frequently Asked Questions (FAQ)

Why are my calculator’s results different from another source?

Small differences can arise from using slightly different values for atmospheric refraction, the exact definition of sunrise (center of sun vs. upper limb), or not accounting for a specific time zone’s daylight saving rules. However, results should typically be within a minute or two.

How do I find the latitude and longitude for my city?

You can use online mapping services. Right-clicking a location on a map will typically reveal its GPS coordinates, which are essential for anyone wanting to calculate sunrise and sunset using latitude longitude.

What happens at the poles?

Above the Arctic Circle and below the Antarctic Circle, there are periods of 24-hour daylight (“Midnight Sun”) in the summer and 24-hour darkness (“Polar Night”) in the winter. During these times, the calculator will indicate that the sun never sets or never rises.

Does weather affect sunrise and sunset times?

No. The calculated times are for a clear horizon. Clouds, fog, or mountains can obstruct the view of the sun, but they do not change the geometrically calculated time of the event.

What is “solar noon”?

Solar noon is the moment the sun reaches its highest point in the sky for the day. It is generally not the same as 12:00 PM on your clock due to time zones and the equation of time. The method to how to calculate sunrise and sunset using latitude longitude is centered around this point.

Why are days longer in the summer?

This is due to the Earth’s axial tilt. During your hemisphere’s summer, it is tilted towards the sun, causing the sun to follow a longer, higher path across the sky, resulting in more daylight hours.

Is the calculation the same for the Southern Hemisphere?

Yes, the math is the same. The only difference is that latitudes are negative, and the seasons are reversed. The formula to how to calculate sunrise and sunset using latitude longitude works universally.

How accurate is this calculation?

For locations below 72° latitude, the calculation is typically accurate to within a minute. Accuracy can decrease slightly at very high latitudes due to the shallow angle at which the sun crosses the horizon.